The crazy Zurich clock

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Swiss readers will immediately recognize in the illustration the abandoned church in a lonely place on the outskirts of Zurich and will remember the curious history of its haunted clock.

Omitting the supernatural and mysterious aspects of the story told to tourists in many versions, we can briefly comment that the church was built in the mid-fifteenth century. It was provided with a watch made by the oldest citizen of the place, a man named Jorgensen, famous for being the founder of the watch factory that gave the place its popularity.

The clock was put into operation at six in the morning accompanied by the ceremony that the Swiss employ in the inauguration of all events, even minor ones. Unfortunately, the clock hands had been mounted on the wrong sprockets. The hour hand began to move while the minute hand marched twelve times more slowly to what the peasants called "the dignity of the hour hand."

After the whims of the haunted watch had been explained to the old and sick watchmaker, he insisted that he be taken to see the strange phenomenon. Due to an amazing coincidence, when the time indicated by the clock arrived was absolutely correct.

This had such an effect on the old man that he died of joy. The clock, however, continued to produce its strange whims and considered itself haunted. No one had the audacity to repair it or to wind it up so that all its pieces were rusting and all that remains of it is the curious problem that I now propose.

If the clock was started at six o'clock as shown in the illustration and the hour hand moved twelve times faster than the other,

When will both hands first arrive at a position where they indicate the correct time?

Solution

The crazy clock will show the correct time again at 7 hours, 5 minutes, 27 seconds and 3/11 of a second.

Loyd does not explain how to get this answer but we cannot resist pointing out how simple the problem is once one has solved the riddle of the clock entitled, "The problem of time." Suppose the haunted clock had 4 hands (a pair that moves correctly and another exchanged). The hands exchanged would only show the correct time when they coincided with the other pair (both hands of the overlapping hours and the hands of the minutes as well).

As one of the pairs is exchanged we can consider that the two hands that indicate the 12 are a hour hand and a minute hand and ask when these two will coincide again. That is precisely the question of the previous problem of the clock whose answer is 5 minutes, 27 seconds and 3/11 past 1. In this case, however, they only give us the position of the haunted minute hand.

We now turn our attention to the pair of hour hands that indicate 6 o'clock and we are in a similar situation. As one of them moves as a minute hand the two will meet again at the same distance after 6 at which the other two hands will meet after 12 o'clock. Hence the answer already cited.)